Pure strictly uniform models of non-ergodic measure automorphisms

Tomasz Downarowicz; Benjamin Weiss

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arXiv · 2104.09604

Pure strictly uniform models of non-ergodic measure automorphisms

Tomasz Downarowicz·Benjamin Weiss

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Abstract

The classical theorem of Jewett and Krieger gives a strictly ergodic model for any ergodic measure preserving system. An extension of this result for non-ergodic systems was given many years ago by George Hansel. He constructed, for any measure preserving system, a strictly uniform model, i.e. a compact space which admits an upper semicontinuous decomposition into strictly ergodic models of the ergodic components of the measure. In this note we give a new proof of a stronger result by adding the condition of purity, which controls the set of ergodic measures that appear in the strictly uniform model.

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Tomasz Downarowicz, Benjamin Weiss. 2021-04-19. Pure strictly uniform models of non-ergodic measure automorphisms. https://arxiv.org/abs/2104.09604

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